Question

You have been scouring The Wall Street Journal looking for stocks that are “good values”

and have calculated expected returns for five stocks. Assume the risk-free rate (rRF) is 6

percent and the market risk premium (rM - rRF) is 2.7 percent.  Which security would be the best

investment? (Assume you must choose just one.)

c. Expected Return = 5.04%, Beta = -0.4, Required Return = 4.92%, Expected Less Required Return = 0.12%

a. Expected Return = 9.01%, Beta = 2, Required Return = 11.4%, Expected Less Required Return = -2.39%

d. Expected Return = 8.74%, Beta = 0.4, Required Return = 7.08%, Expected Less Required Return = 1.66%

e. Expected Return = 11.50%, Beta = 1.5, Required Return = 10.05%, Expected Less Required Return = 1.45%

b. Expected Return = 7.06%, Beta = 0.4, Required Return = 7.08%, Expected Less Required Return = -0.02%

Given the following probability distribution, what are the expected return and the standard

deviation of returns for Security J?

State                      Pi                              rj

1                          0.5                           9%

2                          0.4                           8%

3                          0.1                           27%

10.40%; 5.55%

10.40%; 5.25%

10.20%; 5.35%

10.60%; 5.55%

10.60%; 5.75%

Answer 1

Q1

Expected return should be higher than required return as much as possible.

Required return is the return that justifies the given risk of the security as per the Capital asset pricing model. Expected return is the most likely return based on anlysis of factors like historical returns etc.

So, among the given 5 options, the difference between expected return & required return is highest in option d having expected return (8.74%) - required return (7.08%) = 1.66%. Also its beta is less which implies lower risk. So this would be the best investment.

Q2

The standard deviation can be calculated as shown below:

So the standard deviation is 5.55%

( Note that to avoid decimal numbers while calculating manually, you can also square the deviations without considering the decimal equivalent of percentages i.e. 1.4% squared can be taken as 1.96 and proceed as above, the number that you will get after square root will be the percentage value itself. )

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